But wait! What about the parent class? A Vertex is an Entity, and so I can call any Entity method, too. Maybe there's a transform() method on the Entity class...

Nope.

At this point, you might have given up. (I know I did the first time I tried this...) But don't! The secret is that Entities.transform_entities can accept naked vertices as well as edges and faces. This wasn't obvious to me because if you iterate over the Entities collection, it doesn't contain vertices! So I just assumed that the transform_entities method wouldn't work on vertices. I was wrong, though. It'll accept any Entity, just like the documentation says. Check this out...